Astronomy and Astrophysics – Astrophysics
Scientific paper
2006-01-16
Astronomy and Astrophysics
Astrophysics
26 pages, Transport Theory and Statistical Physics, submitted January 2003
Scientific paper
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical scheme where a Cauchy integral equation is reduced to a couple of Fredholm integral equations. It is expressed in terms of two auxiliary functions $\zeta_+$ and $\zeta_-$ we introduce in this paper. These functions show remarkable analytical properties in the complex plane. They satisfy a simple algebraic relation which generalizes the factorization relation of semi-infinite media. They are regular in the domain of the Fredholm integral equations they satisfy, and thus can be computed accurately. As an illustration, the X- and Y-functions are calculated in the whole complex plane, together with the extension in this plane of the so-called Sobouti's functions.
Bergeat J.
Chevallier Loïc
Rutily Bernard
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